The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  2  2  0  0  0  0  0  0  2  2  2  0  2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  2  0  2  2  0  2  2  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  2  2  0  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  2  2  2  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  0  0  0  2  0  0  0  0  2  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  0  0

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+13x^68+15x^70+35x^72+896x^73+35x^74+15x^76+13x^78+1x^146

The gray image is a code over GF(2) with n=584, k=10 and d=272.
This code was found by Heurico 1.16 in 0.281 seconds.